Actually, I just found the login on the right (Melissa pointed it out), sorry about that.
I just logged in with Facebook and it worked without a problem. My guess is that's because I already had an account. On a separate computer, Melissa wasn't able to login.
However, after I logged in, when I go to the "Private Area", I'm greeted with the 502 Bad Gateway error:
With that, I'm even more confident this isn't a JFBConnect-specific issue, but an underlying server problem. Please investigate what's causing the "upstream prematurely closed connection while reading response header from upstream, client:" errors in your logs and I think you'll be able to find the issue.
Thanks,
Alex